I've seen songs analysis that says a song is in determined key even when the root is not played once in the whole song, how does this works? I understand that by listening how the song resolves I can know the key, but its there any rule?

marked as duplicate by Dom♦ theoryUsers with the theory badge can single-handedly close theory questions as duplicates and reopen them as needed.Jun 25 at 19:12

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I would rather ask: what bad would happen if I considered C and Am practically the same key. What good might happen as a result? What bad would happen, if I couldn't tell with 100 % certainty, what the key "is" at each moment of the progression? Would it be bad if the progression couldn't be said to be in a single key from beginning to end? What is it that you want: make music, or gain status and respect among theory geeks? ;) The "is the key C or Am" question is largely an academic one.
– piiperiJun 25 at 18:03

well, im just curious about how it works, im self-tought , and now i want to profundize on theory cuz i want to play songs by earing (not just looking for the tabs or chords in ultimate-guitar) then this doubt came up... i mean ive seen those people that know the songs key just by listening (even when the root note is not played in the whole song).. and i want to learn to do that for myself
– JeffCasinoJun 25 at 18:09

@piiperi - V>I (or V>i or even v>i) is a very strong cadence. happens in most pieces at some (or many) points. In C it's G>C. In Am it's E>Am. E isn't diatonic, so would give a rather different feel.
– TimJun 25 at 18:09

@JeffCasino - it's pretty unusual that a song would be conceived to be in a key where that root note/chord was never played.
– TimJun 25 at 18:11

@Tim so i just need to listen and get familiar with cadences then i would be able to identify dominant, subdominant and deduce the key... thanks to all
– JeffCasinoJun 25 at 18:17

2 Answers
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Saying that a piece of music is "in a key" often (even usually?) isn't a statement of fact, but a statement of perspective.

When you say that a piece is in C major, you're saying that

The tonal centre of the piece is C - that you mostly feel that C is the home note

The set of notes used by the piece is a reasonable fit with the C major scale - that the notes C, D, E, F, G, A, B are the framework that the piece is built around.

The thing about both those statements is that they leave some room for opinion - they are not absolute, factual statements.

I compose a chord progression F-G-C-Am … can I assume C as the Key?

Not necessarily. It depends on the phrasing of those chords. If Am is the most important chord in the phrasing, then it might sounds more to you like A minor. You have to think whether you feel that C, or A, or something else is the 'home note'.

how do I know I'm not in Am

You can't "know" - but you can feel that the piece doesn't come home to A.

I've seen songs analysis that says a song is in determined key even when the root is not played once in the whole song, how does this works?

Because key is a question of perspective, not a question of fact, you can analyse any song from the point of view of any key. It might be useful and interesting to analyse a given piece from the point of view of a key for which the song didn't land on the tonic chord. In such cases, it's unlikely that that would be the only sensible key to think about.

is there any rule?

No, no absolute rule. People often come up with "rules of thumb" that work for them, but none of them are definitive.

The one way in which being "in a key" could be definitive is if the composer labels it as such - e.g. if I write "Scherzo and Trio in A minor", then in that sense it is defined to be "the key" of the piece. But I don't think that's the sense in which you ask the question.

One shows a key by the main cadences in the piece; especially at the end of the whole composition. Some internal cadences (at the end of phrases or sections matter too.)

If a piece is in C-major, the piece will probably end with an authentic cadence on a C-maor chord; usually the pattern G-C or G7-C or dm-G-C or dm-G-G or F-G7-G something similar (ii-V-I or IV-V-I).

The cadence generally has a pre-dominant chord (or subdominant, depending on who's doing the analysis), a dominant chord (maybe with a 7th) followed by the tonic chord. Symbolically one has S-D-T (subdominant, dominant, tonic). S stands for things like ii, ii0, ii6, IV; D stands for V or V7, and T for I in a piece-ending cadence.

In a minor key, the same pattern occurs, S-D-T where S now may be iv or ii0 or ii06 etc, and D is V or V7 (just as in the parallel major) and T as i.

So if the piece ends with a G-C chord pattern perhaps preceded by a dm or dm6 or F major, the piece (or at least the previous section) is in C-major.

If the piece ends with an E-a or d-E-a or f#0-E7-a, etc. the piece is in A-minor.

Key can feel clearly-established by cadences, but then there are also lots of pieces that don't feature clear cadences - lots of pop, rock, and techno pieces are based around repetitive chord sequences that don't seem to have clear cadence points.
– topo mortoJun 25 at 19:07